Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
191
When $19^{300}$ is divided by 20, find the remainder. (a) 2 (b) 1 (c) 3 (d) 4
Answer:
1
We can use the concept of modular arithmetic or the remainder theorem.
192
If 3 is added to each odd digit and 2 is subtracted from each even digit in the number 6452851, what will be the difference between the largest and smallest digits thus formed? (a) 8 (b) 6 (c) 4 (d) 2
Answer:
8
**Step 1:** Apply the rules to each digit of the number 6452851.
193
If $3x^2 + ax + 4$ is perfectly divisible by $x - 5$, then the value of a is: (a) - 12 (b) - 5 (c) - 15.8 (d) - 15.6
Answer:
- 15.8
According to the Remainder Theorem, if a polynomial $P(x)$ is perfectly divisible by a linear factor $(x-c)$, then $P(c) = 0$.
194
What is the value of the digits A and B? $BA \times B3 = 57A$ (a) A = 2, B = 4 (b) A = 3, B = 5 (c) A = 5, B = 2 (d) A = 5, B = 3
Answer:
A = 5, B = 2
This is a cryptarithmetic puzzle. We can solve it by testing the given options.
195
Find the largest number of four digits that is completely divisible by 49. (a) 9998 (b) 9994 (c) 9992 (d) 9996
Answer:
9996
**Step 1:** The largest four-digit number is 9999.
196
When the number $(5)^{501}$ is divided by 126 then the remainder will be? (a) 117 (b) 121 (c) 89 (d) 125
Answer:
125
We will use modular arithmetic. We need to find the remainder of $5^{501}$ when divided by 126.
197
$276x1$ is divisible by 3. What is the sum of the possible values of x? (a) 18 (b) 21 (c) 12 (d) 15
Answer:
15
For a number to be divisible by 3, the sum of its digits must be a multiple of 3.
198
If the 8-digit number $3x5479y4$ is divisible by 88 and the 8-digit number $425139z2$ is divisible by 9, then find the maximum possible value of $(3x + 2y – z)$. (a) 33 (b) 37 (c) 25 (d) 35
Answer:
33
This problem has two parts.
199
Which of the following numbers is NOT divisible by 8? (a) 35792 (b) 35112 (c) 35412 (d) 35552
Answer:
35412
The divisibility rule for 8 states that a number is divisible by 8 if its last three digits are divisible by 8. We will check the last three digits of each number.
200
The smallest positive number which must be added to the greatest number of 4 digits in order that the sum may be exactly divisible by 307 is: (a) 307 (b) 132 (c) 306 (d) 176
Answer:
132
**Step 1:** The greatest 4-digit number is 9999.